Structure of the set of all minimal total dominating functions of some classes of graphs

In this paper we study some of the structural properties of the set of all minimal total dominating functions (${\displaystyle \_T}$) of cycles and paths and introduce the idea of function reducible graphs and function separable graphs. It is proved that a function reducible graph is a function separable graph. We shall also see how the idea of function reducibility is used to study the structure of ${\displaystyle \_T\left(G\right)}$ for some classes of graphs.